Sr Examen

Derivada de y=tgx*arcsinx

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
tan(x)*asin(x)
$$\tan{\left(x \right)} \operatorname{asin}{\left(x \right)}$$
tan(x)*asin(x)
Gráfica
Primera derivada [src]
   tan(x)     /       2   \        
----------- + \1 + tan (x)/*asin(x)
   ________                        
  /      2                         
\/  1 - x                          
$$\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)} + \frac{\tan{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
Segunda derivada [src]
  /       2   \                                               
2*\1 + tan (x)/     x*tan(x)      /       2   \               
--------------- + ----------- + 2*\1 + tan (x)/*asin(x)*tan(x)
     ________             3/2                                 
    /      2      /     2\                                    
  \/  1 - x       \1 - x /                                    
$$\frac{x \tan{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{asin}{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{1 - x^{2}}}$$
Tercera derivada [src]
  /          2 \                                                                                              
  |       3*x  |                                                                                              
  |-1 + -------|*tan(x)                                                                                       
  |           2|                                                        /       2   \     /       2   \       
  \     -1 + x /            /       2   \ /         2   \           3*x*\1 + tan (x)/   6*\1 + tan (x)/*tan(x)
- --------------------- + 2*\1 + tan (x)/*\1 + 3*tan (x)/*asin(x) + ----------------- + ----------------------
               3/2                                                             3/2              ________      
       /     2\                                                        /     2\                /      2       
       \1 - x /                                                        \1 - x /              \/  1 - x        
$$\frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\sqrt{1 - x^{2}}} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \tan{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$$
Gráfico
Derivada de y=tgx*arcsinx